Hello everyone. I'm new here. I have a practice test that I'm working on for my linear algebra class and I sorta get the gist of determining whether or not something is a subspace or not but I'm having trouble with this one:
I did terrible in Calc 2 so the whole derivative thing isn't too familiar to me.
As you would prove any such fundamental statement- from the definition:
f+ g is defined as the function such that (f+g)(x)= f(x)+ g(x).
Similarly, g+ f is defined as the function such that (g+f)(x)= g(x)+ f(x).
Saying that f+ g= g+ f is just saying that, for all x, f(x)+ g(x)= g(x)+ f(x) - and that's true because f(x) and g(x) are numbers and addition of numbers is commutative.